Cable that holds the elevator got disconnected

[UltraPi1]

Even when your body is in the act of flying upwards while jumping inside of the falling elevator, this speed is simply subtracted from the speed that the elevator is falilng,, so you would ultimately still be falling down very fast.

This what I was trying to get across to Integral. I said if you were super human - you could negate that speed entirely. He seems to think otherwise. In fact he insist you would hit ground zero faster than the elevator.
In the real world - you would be in deep dodo ... no question about it. The original question of the thread was whether jumping could make a difference.
Under the right conditions - In the real world - It could.

 

[Integral]

Mr. Ultra pi,all leg muscle and no brain, at least after you mash your head into the ceiling of a falling elevator. Yes, if you could jump with a velocity equal to that of the falling elevator there would be a point at which you would have zero velocity with the outside world, unfortunatly that would probably mean that you will meet the ceiling of elevator with a relative velocity twice that (very nearly at least) at which the elevator is traveling. I thought the point of the question was can you save yourself by jumping. The answer remains no, you have simply added another way of dying.

 

[Gara]

that's what I've been saying! IF you had super strenth you could do it.

and i acually think you won't hit your head, if you jump up at the same speed the lift is going down, asuming as you hit the apex, (0 mph) the lift hits the bottom and stops moving, then you just free fall the tiny distance to the floor.

i suggest that since this is all about IF, it should be moved to the thory section.

 

[UltraPi1]

Mr. Ultra pi,all leg muscle and no brain, at least after you mash your head into the ceiling of a falling elevator.

A properly timed jump with the appropriate force, and you would not hit the ceiling. In fact you wouldn't have to leave the floor. All you have to do is equal the speed of the falling elevator, thereby canceling out. This is all under optimal conditions mind you. Wrong again.

I thought the point of the question was can you save yourself by jumping.

And I have said - Under the right conditions - it could make the difference ... however small it is. Even without super human legs. I said at the beginning of this thread ... Parameters would have to be set to answer that question. How big is the elevator? How much does it weigh? How well sealed is the shaft? How much space is there between the elevator exterior to the shaft walls?

 

[Integral]

A properly timed jump with the appropriate force, and you would not hit the ceiling. In fact you wouldn't have to leave the floor. All you have to do is equal the speed of the falling elevator, thereby canceling out. This is all under optimal conditions mind you. Wrong again

This is getting to be pure nonsense, where do you get this stuff from?

If your feet never leave the floor of the elevator then you are traveling the same speed as the elevator .. going DOWN! If you wish to cancel the speed of the elevator you must jump UP, now the only thing you have to push against is the FLOOR of the elevator. If you apply a force to the FLOOR you will accelerate with respect to that floor. So applying a force to the floor and staying at rest wrt that same floor is nonsense.

What is important here is your speed wrt to the ground, if you can hit the ground with speed approximately 0 then you will be fine. This means you must have a velocity wrt the elevator of V up.

Now a good question is what is a fatal velocity, is a 20m drop fatal? Maybe not, but I would not want to try it. A bit of computation shows that

v = \sqrt {2gx}
This gives a value of ~20m/s for a 20m fall. It is humanly impossible to cancel a fall at this rate. Unless you are a pretty good athlete a standing jump of .5m is pretty good, to jump .5m you need an initial velocity of about 2.25m/s.

Needless to say even for 10m/s fall a perfectly timed jump up at 2.25m/s will not help.

 

[UltraPi1]

This is getting to be pure nonsense, where do you get this stuff from?

It would seem you're going to fight this one all the way to the ground. Which is about where you got to make yer jump. I might as well call you pig headed .. with wings of course. You would hit the ceiling if you didn't time your jump. If the elevator were dropping at 70MPH and you made your jump 30 feet before you hit ground, and you were capable of jumping fast enough and hard enough to cancel the fall. You would hit the ceiling in the neighborhood of 70 MPH - (propably faster).

You would likely make your jump in the vicinity of 3 feet off the ground. Using your super human legs mind you. At the same instant you finish with the appropriate jump - The elevator hits ground. All things perfect - All things canceled. It would be as if nothing happened. Accept for the very loud boom at ground zero. Since the elevator is no longer dropping - Theres no need to worry about the ceiling because you are dropping at 0 MPH in relation to the ground due to your canceling jump, and the elevator is dropping at 0 MPH because it hit ground.

Now a good question is what is a fatal velocity, is a 20m drop fatal? Maybe not, but I would not want to try it. A bit of computation shows that

Yes ... that would be a good question regarding a personal drop in a free falling elevator. The most important parameters to consider would be the weight of the elevator, the surface area of the floor, how much space is there between the outside walls of the elevator and the shaft walls, is the shaft sealed well .. below the elevator? I would get in an elevator that had one eighth inch clearance between the exterior walls of an elevator and the shaft walls --- in a free fall. Providing there was no escape for the air below the elevator other than the one eighth clearance. It could very well be used as a ride at an amusement park.

Now to the real world elevator. How fast will it drop? This can't be set without setting parameters for it. I'm sure there are some elevators out there where if all the safety installs failed. You could expect a decrease in velocity toward the end of your ride before you hit ground, and there are some elevators out there where you could kiss your ass goodbye in a complete system failure. Now should you ever run into this kind of situation - I say jump ... Go ahead and jump, because you aint got time for love in an elevator. :-)

 

[outandbeyond2004]

I assume someone is atop on a block of metal that is freefalling towards an airless planet the mass of Earth. The block and the person has masses m_B and m_P, which are negligible compared to the mass of the planet. So, from

conservation of momentum

(m_P + m_B)v = m_Pv_P + m_Bv_B

and conservation of energy (potential energy can be ignored as this is instanteous change of energy)

(m_P + m_B)v^2 = m_Pv_P^2 + m_Bv_B^2

where v, v_P, v_B are respectively the initial velocity, the velocity of the person at the moment of final velocity change caused by the jump, and the velocity of the block at the moment of final velocity change caused by the jump.

Solve for v_P:

v_P = \frac{(m_P + m_B)v^2 - m_Bv_B^2}{(m_P + m_B)v - m_Bv_B}

Let

v_B = \gamma v

and

\kappa = \frac{m_B}{m_P + m_B}\gamma

The equation for v_P can be rewritten:

v_P = v\frac{1-\kappa\gamma}{1-\kappa}

It is now evident that by some judicious combination of values for \kappa and \gamma we can have any value for v_P including escape velocity away from the planet.

 

[chroot]

Integral is fully correct. Even if you could jump, and even if there were no ceiling in the way, you would go up, and eventually land with the same velocity the elevator landed. All you could do is delay the impact slightly. You can't beat the conservation of energy.

- Warren

 

[Integral]

First of all, in a properly designed elevator, this is simply not a problem, so why are we even thinking about elevator design? Remember the original question, it concerns a falling elevator in which the passenger is in danger (I assume this 'cus otherwise there is no question).

Therefore we have an elevator falling at a dangerously high speed, particulars of the elevator are not important. What is this speed and how does it compare to the speeds which a jumping human can hope to generate? By my estimates "dangerously fast" will be anything from about 10m/s up. 10m/s sec is equivalent to a free fall drop of 5m (This is a survivable drop, but I personally would not want to jump from 5m onto concrete (water is ok!)as serious injury is possible (even in water if you hit wrong!).

Ok, now to completely cancel the elevators velocity a human would have to jump up wards at precisely the right time with a velocity equal and opposite to that of the elevator. How many people do you know that can do a standing vertical jump of 5m? It is virtually impossible to cancel the velocity of even a survivable fall rate.

Now on top of this comes an additional problem, when to jump, in order to cancel the elevators velocity you must have the maximum upward velocity at the instant the elevator hits the ground, now the million dollar question is... How do you know when the elevator is going to hit? This is information that is not available, so I am right back to my origin statement... Jumping will not help. Simply because it is not enough and impossible to time correctly.

 

[chroot]

And, to reiterate my point, even if you could jump up from the floor of the elevator at 10 m/s and thus avoid being killed by the fall, you would eventually land at 10 m/s anyway, and die just a short time later.

- Warren

 

[Integral]

A key point here is that when falling at a velocity V, your body had kinetic energy mV²/2 it does not matter whether this energy is dissipated by jumping or stopping the effects on your body will be the same.

 

[Janus]

One thing that seems to be missed with all this super-human legs business. Your body would still have to absorb the forces involved in coming to a stop. It would just be spread out over the distance over how much you can bend your legs.

For instance, assuming you are trying to cancel out a falling speed of 60mph (88 ft/sec) and you maximum leg flex is 2 ft (from crouch to extended), the rest of your body would have to be able to withstand 60g. (forget about what happens later, the jumping itself would kill you.)

To survive, you would need a combination of enough leg strength and g force resistance. But if you had these, then you don't need to jump in the first place. You can just allow yourself to go from standing up to a crouch as you hit and let your legs absorb enough of the deceleration(like a shock absorber) to let you come out unharmed.

 

[outandbeyond2004]

A post considered jumping hard enough to cancel the downward speed. That is not possible if my equations in a prior post are correct. Substitute zero for v_P and solve for v_B. The result is the same as the downward speed just prior to the jump. This is possible only if the mass of the person is zero.

You can survive any value of personal KE as long as you have time to dissipate it. However, a jump certainly does not give you much time, and if you have to jump to dissipate mucho KE, that would HAVE to be a very, very brief jump. It is said that people can survive 20 Gs, but I rather doubt even Olympic-class athletes can match that by jumping. Barry Sanders, the football carrier -- nah.

So I agree that jumping will do little good, and maybe it would be better to get to the top of the elevator, if at all possible, in the hope that the elevator can cushion the impact well enough.

A racecar driver survived a 170mph crash, because the "cell" he was inside absorbed enough energy slowly enough to let him survive.

 

[UltraPi1]

Integral is fully correct. Even if you could jump, and even if there were no ceiling in the way, you would go up, and eventually land with the same velocity the elevator landed. All you could do is delay the impact slightly. You can't beat the conservation of energy.

Wrong also. When you jump - You are just transferring that potential energy from you to the elevator through the use of another energy source, and that would come from those superhuman legs.

 

[Integral]

Wrong also. When you jump - You are just transferring that potential energy from you to the elevator.

What potential energy? Potential energy is not a problem,the problem is kinetic energy.
Can you explain the difference between the elevator suddenly stopping and you jumping? If you change your velocity from -V to 0 the change in velocity is the same, Remember the old saying "Its not the fall that hurts, its the sudden stop at the end". It does not matter what causes the sudden stop the forces experienced by your body will be identical in either case.

You need to read some of the other posts.

 

[UltraPi1]

One thing that seems to be missed with all this super-human legs business. Your body would still have to absorb the forces involved in coming to a stop. It would just be spread out over the distance over how much you can bend your legs.

Not missed - Just not mentioned. Make no mistake about it. This is a job for a superhuman. But you seem to at least understand the process of being able to slow your descent to zero by taking the hit before ground zero. Some here do not.

 

[UltraPi1]

Can you explain the difference between the elevator suddenly stopping and you jumping? If you change your velocity from -V to 0 the change in velocity is the same, Remember the old saying "Its not the fall that hurts, its the sudden stop at the end". It does not matter what causes the sudden stop the forces experienced by your body will be identical in either case.

You seem to be evading the original disagreement from the content of your last few post. I'll take that as a ... yes .. I was wrong, and accept that you just don't want to say so. At any rate I'm done here.

 

[Integral]

slow your descent to zero. Some here do not.

How do you SLOW you decent. You have only mentioned how to change it SUDDENLY, it is the sudden part that causes problems.

 

[Michael D. Sewell]

Originally posted by Integral
By my estimates "dangerously fast" will be anything from about 10m/s up. 10m/s sec is equivalent to a free fall drop of 5m (This is a survivable drop...

Integral,
This is a very good estimate. You are even being a little generous. In skydiving we consider 3m/sec to be a safe rate of descent for landing; higher speeds are OK with proper technique if the jumper is in excellent physical condition.

In construction, falling two stories is considered to be survivable. Falls involving distances greater than that rapidly decrease your chances for survival. This is a well documented fact. -Mike

 

[Integral]

Michel,

Thanks for the infromation. I spent a bit of time searching for real data with no luck, finally just aked myself how far would I want to jump. In my youth I did a fair amount of jumping off rocks into water, I know that anything over about 5m takes courage (or lack of brains!).

I find it interesting that your safe landing speed is very close to the landing (and launch) velocity of a good jump.

 

[Michael D. Sewell]

You mentors take a lot of abuse, a big thank you to all of you for your contribution to the physics forums. -Mike

 

[outandbeyond2004]

Originally posted by Michael D. Sewell
You mentors take a lot of abuse, a big thank you to all of you for your contribution to the physics forums. -Mike

Amen!

 

[Cliff_J]

Agreed with above. Its more a question of if you restrict the elevators speed to a human attainible number OR if you're willing to consider a world where humans could be 2-3 orders of magnitude stronger to 'push off the elevator floor' (jump) hard enough to create a velocity with an opposite vetor component and the soft tissue could handle the loads as well). I thought it was humorous to joke about it, maybe not.

What if we change this to a problem of solving how much potential energy we need to store in a spring along with the timing and duration of energy release to push a 30Kg weight off the floor of our falling elevator that weighs 2 metric tons. While this would not be a trivial integration to solve, it seems like an equivalent problem that doesn't fall prey to human strength limitations, correct?

Cliff

 

[Gara]

im confused. are some of you saying that if i am on a surface which is falling at 60 mph, and i jump up so i am now falling at 0 mph in relation to the ground outside, i would still land at 60 mph?

even if the ground is 5 feet below me? how am i going to accelorat in a free fall to 60 mph with in the distance of 5 feet?

 

[Integral]

No we are saying that if you were falling at 60mph and jumped so your speed was 0 your body would be every bit as crushed as if you had let the ground stop you.
edit:
Forgot a bit.


Now let us suppose that the elevator is falling at a constant velocity.(I am going back to metric, just because.) Also I am going to totally neglect any superhuman feats, So the elevator is falling at a dangerously fast constant velocity, say 20m/s. If at some random time during the fall you jump up wards with an initial velocity of 2m/s your equation of motion wrt to the elevator will be given by y= 2t- gt²/2. You velocity will be given by v= 2-gt. The max height of the jump will occur when the velocity is 0 or at t= 2/g (let g=10 for easy numbers) so t~.2s. Now at the peak of your jump your velocity wrt elevator =0 at that point you begin to fall back to the floor of the elevator your velocity is still described by v=2-gt but now we have gt>2 so your velocity is negative. That is you are moving down.

Now let us superimpose the motion of the elevator on the motion of the jump. This is what an outside observer would see.

V_elevator + V_you = -20 + 2 -gt = -18-gt.

The first thing to notice that there is no value of t for which this is a positive number, so you are ALWAYS falling. For the time period (0,.2) your velocity will be less then 20m/s, at t=.2 your velocity will BE 20m/s (remember we have 0 velocity wrt to the elevator) for t > .2s you velocity will be GREATER then 20m/s as you will be accelerating in free fall motion until you reach the floor of the elevator. This would occur at t=.4s, at that time your velocity will be 22m/s.

OK, so there it is, during the period (0,.2s) you have succeeded in reducing your velocity wrt to the ground. Now, consider that you MUST be in the air when the collision occurs, the further into that initial .2s you are the faster you are falling, consider the condition of your legs at the instant you jump, they are fully extended, knees straight and perhaps locked, this looks like the way to MAXIMIZE injury, especially since you are still falling and will impact the ground before completion of the jump.


I still maintain that jumping will do no good.

 

[outandbeyond2004]

Gara, to amplify Integral's reply a bit:

If you could jump SLOWLY enough and yet attain zero velocity (something that my equations show is possible only for a person with zero mass) then ultimately you will go far above the ground. Then there is nothing left to do but a Wiley Coyote and no elevator to jump off. But nobody can jump slowly, no leg is long enough. And, if you can jump fast enough, your leg bones will tear into small bits, to say the least. Maybe death will be by internal bleeding in the thigh. Actually that is not all. Forces induced by such tremendous acceleration (exceeding 20 Gs, probably) must do a lot of havoc to other parts of the body, such as the brain; maybe it will turn into . . . well, enough.

 

[Gara]

aah i see now.

so the asnwer is,

Only if you SOMEHOW knew where the bottom was, and somehow knew how FAST the lift was falling, and knew JUST when to jump, and had SUPERHUMAN strenth, to be able to jump up at the speed of the lift is falling at a speed you do not know, and if you timed it just right, even though you don't know where the bottom is, you could slow to 0 mph, making the same G Forces as if you had just crashed, meaning you might as well just crash.

so basicly, you can only survive it by jumping, if you are able to survive it by crashing. making the jump pointless.

 

[Michael D. Sewell]

Gara,
You've just made us all very proud.

 

[AnthreX]

i am very confused with all these conclusions..

can someone tell me what the real conclusion is?

or .. is the argument still continuing ?
ta

 

[Integral]

Read Gara's last post, she sums it up nicely.

 

[Rog]

I always thought that the reason you would die in such a scenario is due to deceleration trauma i.e. when the elvator hit the ground your organy soft bits would continue and try and take up residence in your legs! So by this thinking even if you could jump at the quoted 60mph you would reduce the impact on landing however you would have experienced the deceleration trauma you were trying to avoid by the very act of jumping.

 

[Cliff_J]

Anyone of us can jump off a building and land on an airbag and live to tell about it. Same velocity/kinetic energy/etc, longer timeframe=lower G loads=survivability.

So unless your fast twitch muscle fibers are really fast, seems pretty slow in comparsion of a steel on concrete impact. So I respectfully disagree that it won't help to jump, although I think we can all agree it becomes a mere formality after a certain speed is attainted.

Cliff

 

[UltraPi1]

Cliff has it right. You would still be better off jumping. Jumping would allow you to absorb the energy of the fall over the course of say two feet, while not jumping requires you to absorb the impact in one feld swoop. Irrespective of whether you survive or not - Jumping at the right moment has a greater chance for survivability than not jumping.

 

[outandbeyond2004]

Well, there may always be borderline cases when it is better to jump. But, generally speaking . . .

 

[Integral]

The more I look into this the more convinced I am that jumping, not only will not help but may well be the formula to maximize injuries. Simply because, to reduce your fall velocity, you must jump less then about .2s before impact, this means, since you are really still falling at a pretty good rate, you will impact with your legs straight and knees locked. Not what you want. Your best bet may to to lay flat on floor and adsorb the shock with as much surface area as possible.

I am not sure what air bags and cushioned landing have to do with this discussion. If those safety features are in place then you were never in danger to begin with, so why bother jumping

 

[UltraPi1]

Your best bet may to to lay flat on floor and adsorb the shock with as much surface area as possible.

Bad idea - The main thing to protect is your head. Your legs are expendable. They can serve to absorb some shock albeit little. You might as well let someone take a full swing to your head with a baseball bat than lie on the floor. Ouch!

 

[jdavel]

Janus wrote: "To survive, you would need a combination of enough leg strength and g force resistance. But if you had these, then you don't need to jump in the first place. You can just allow yourself to go from standing up to a crouch as you hit and let your legs absorb enough of the deceleration(like a shock absorber) to let you come out unharmed."


I think you're forgetting something. If you jump you get to use the fles in your legs twice, once when you jump and once when you land. So whatever maximum deceleration the rest of your body has to absorb is cut in half. Since no one has enough leg strength to produce a lethal acceleration by jumping, any jump that has you moving away from the floor when the elevator lands will improve your chance of survival.

 

[outandbeyond2004]

In the case that the elevator is already going too fast or will, I think it would be better to flex your legs and hip at about 160-170 degrees and brace your arms straight downwards than trying to time your jump. We should not expect the person atop the elevator to be able to see the end coming well enough to time the jump, if it would help at all.

I wrote the above before seeing jdavel's post. I assume he had in mind jumping before the elevator hits. If so isn't he forgetting that any KE that is dissipated by the jump would soon be restored, and the end would be about just as bad anyway. The potential energy is the same however and when you jump. Otherwise, if you jump right at the moment the shock of the elevator's ground impact reaches just a few centimeters above the level where your feet are (or maybe 6-10 cm depending on how long your legs are), I don't think it would really be a jump. The neuromuscular-skelton system, if not badly damaged enough, would have its coordination too badly disrupted to generate much power for a jump. However, suppose it did manage a really good jump, i.e., not only did it absorb and dissipate considerable KE in heat (damages the muscles etc.) and muscle tears, you have to do it again ==> Yet more heat in already damaged and torn muscles, etc.

 

[Integral]

If you can understand the analysis I did up stream a bit you will understand why your legs will NOT be flexed for the landing following a jump. The time to reach the peak of a normal humans standing jump is roughly .2s this corresponds to an initial jump velocity of 2m/s. So if the elevator, falling at say 10m/s hits bottom shortly after your feet leave the floor, you will still be falling at a rate of about 8m/s. Let us suppose the elevator hits the ground when you your feet are 5cm off the floor. Let's run some numbers on this.

With respect to the elevator we have

y= 2t -gt² = .05

This occurs at .03s from the time you feet left the floor. At this time your velocity wrt to the elevator is 1.7m/s but, remember the elevator has just come crashing to a stop, all that remains is your velocity wrt to the outside world which is -8.3m/s, now you are .05m from the floor, your legs are still configured for the jump you just initiated. According to my numbers you are .007s from hitting the floor traveling at over 8m/s, this equivalent to a free fall from about 12.5m.

Edit:

This in incorrect it should read 3.3m

End edit


You are now in just about the WORST possible ergonomic condition for surviving such a fall. How will having your thigh bones driven into your shoulder blades protect your head? Knees? what knees?
Think about it.
Edit:
from only 3m you would probably only break your legs

End edit.

Once again, jumping is NOT the thing to do.
I think that I would prefer doing this standing on my head, It would be over with in a hurry that way.

 

[outandbeyond2004]

Warning = although this has been edited, it may still offend some people.

Some of Integral's number seem to be incorrect, and we have overlooked the effect of adrenaline ==> superhuman athletic feats.

Let me add here to the advice to get to the top if at all possible. If the elevator crumples to a pancake, you certainly don't want to be inside. One way to get to the top is to take your shoes off and fling them to the floor one at a time. However, if you have time to do that, well, good luck!

I assume Integral is correct to say that most young adults can manage jumps with an initial velocity (feet just leaving the ground) of 2 m/s. I will try 4 m/s just for fun if nothing else.

I also assume the elevator is falling at 5 m/s. I think after reading Integral and from my memory, this is survivable for most people; but the question now is, would jumping make your landing easier?

I assume you have managed to somehow climb onto the elevator's top. You time the jump just before the elevator top comes to a rest, which may be 3 m above the ground, but you are still moving at 5 m/s wrt the ground. This is just before the shock reaches your feet, not like in my last post. (The elevator top might even bounce up a little.) So, wrt the elevator top just before it comes to a stop, which after all is what you will impact with, the position of your head is maybe

y = 1.5 - t - gt^2/2

where t = 0 is the time of maximum velocity, when your legs are almost straight and your feet is still in contact with the elevator top and at zero velocity wrt the elevator. I suspect that is pessmistic, because surely the elevator top will begin to slow down shortly after the elevator bottom hits the ground.

You have been following the thread, so you know at this point that you have to immediately tense your thigh muscles to brace yourself. How much time do you really have? Just 0.2 seconds to recognize that you have successfully timed your jump and to tense your thigh muscles, according to computations from the above equation. At this point, your head would have moved down about 0.4 meters. You can't generate much power in this position in the time left till head impact, which is about 0.3 seconds, so your legs are going to bang against the elevator top. Ouch! You will hold out your hands to break your fall.

I am going to disagree somewhat with Integral. Surely survival of the head takes precedence over that of the limbs. He may have overlooked the point that the head attains maximum velocity while the feet is still in contact with the elevator. The person's center of mass might move less than the head during the jump, besides, which would make a difference in boderline cases.

So in conclusion, well, I don't know about the borderline cases. Maybe jumping will be better, and in other cases maybe not.

 

[Michael D. Sewell]

Originally posted by outandbeyond2004
we have overlooked the effect of terror ==> adrenaline ==> superhuman athletic feats.

For me to agree with you on this statement, you are going to have to modify it by changing the word "terror".

I can tell you that during years of skydiving and flying, I have seen many, many times, the "effect of terror" on human beings. The "effect of terror" is as follows: the terrorized person assumes the fetal position immediately, and stays in that position for several seconds, sometimes many seconds. Any attempts to communicate with the person during this time are futile. The terrorized person is in his or her own little world. If the terror passes; then, and only then, will the person begin to take steps to save his or her life.

In your elevator situation you would almost certainly be totally terrorized, and almost certainly found on the floor of the elevator, in the fetal position.

I don't want to hurt anyone's feelings here, but in my opinion, a discussion such as this should take place in a sandbox on a playground, not in the physics forums. Please close this thread.
-Mike

 

[outandbeyond2004]

I apologize if I have offended anyone by anything like a poor choice of words or by the tone of my writing. Besides, my attempts to produce witticisms and amuse people were perhaps misplaced.

 

[jdavel]

Integral said:

"If you can understand the analysis I did up stream a bit you will understand why your legs will NOT be flexed for the landing following a jump."

I think I understand your analysis, but I think you've made some mistakes. For example, you say:

"With respect to the elevator we have y= 2t -gt2 = .05"

I don't think this is correct. In this equation, t refers to the time interval that begins when my feet leave the floor and ends when they are .05m off the floor. But during that time the elevator and I are both in free fall, so my speed "with respect to the elevator" is not accelerating at g; it's a constant, namely 2(m/s). So the equation to find t is just:

y = 2t = .05m

Then you said this:

"According to my numbers you are .007s from hitting the floor traveling at over 8m/s, this equivalent to a free fall from about 12.5m."

I don't think this is correct either.

v(s) = sqrt(2gs)

It looks like you've dropped a factor of two somewhere; velocity should be more like 16(m/s).

I do agree with the 2(m/s) you used for a reasonable jumping speed. But that speed will come off your landing speed as long as you wait to jump until you're falling at a speed of at least 2(m/s). The problem is that 2(m/s) isn't very much, unless the fall is pretty short. Even from your 12.5m (about 40ft) you'd hit the ground at 16(m/s). A 2(m/s) jump cuts that to 14(m/s), better, but still pretty painful!

The reason this problem got so complicated is that we all mixed physics with physiology.

I think the pure physics is this. Two masses are in free fall with one just above the other. The total momentum transferred to the Earth when both masses have landed, has to be the same, no matter what happens on the way down. If at anytime during the fall, the top mass can increase the downward speed of the bottom mass by applying a downward force to it, then the bottom mass will transfer more momentum to the Earth than it would have, so the top mass will transfer less and land more gently than it would have. It doesn't even matter when the force is applied (again, as long as applying it doesn't cause the top mass to start moving away from the ground).

I think the physiology part is this: The best survival strategy is to give as much of your momentum as you can to the elevator and then bend your legs so that the impulse, integral(Fdt), that you apply to the Earth is spread over the maximum possible time, thus requiring the minimum possible force. But if the fall is from more than about 50 ft, even doing both of these won't prevent a pretty serious injury.

 

[outandbeyond2004]

I have been wondering if one should jump as soon as possible then try to use air resistance. Spread out your coat, e.g.; bump against walls. Maybe you can catch the edge of a floor that is a little past the floor's elevator doors. Yeah, that's what I'd try to do once I got to the top, try to land in a floor cavity behind some elevator doors. Even if you fall out, you can greatly slow your descent that way.

 

[Integral]

Integral said:

"If you can understand the analysis I did up stream a bit you will understand why your legs will NOT be flexed for the landing following a jump."

I think I understand your analysis, but I think you've made some mistakes. For example, you say:

"With respect to the elevator we have y= 2t -gt2 = .05"

I don't think this is correct. In this equation, t refers to the time interval that begins when my feet leave the floor and ends when they are .05m off the floor. But during that time the elevator and I are both in free fall, so my speed "with respect to the elevator" is not accelerating at g; it's a constant, namely 2(m/s). So the equation to find t is just:

y = 2t = .05m

Absolutely NOT. If the elevator is falling at a constant velocity you can jump up and down on it all day long and not know that it is moving, it will seem as if you are on a stationary floor.
My equations are correct and the time is correct

Then you said this:

"According to my numbers you are .007s from hitting the floor traveling at over 8m/s, this equivalent to a free fall from about 12.5m."

I don't think this is correct either.

v(s) = sqrt(2gs)

It looks like you've dropped a factor of two somewhere; velocity should be more like 16(m/s).

You are correct here, it is not a missing factor it is reading the wrong numbers out of my spread sheet. actually is is only a fall of about 3.5m which is survivable.

I do agree with the 2(m/s) you used for a reasonable jumping speed. But that speed will come off your landing speed as long as you wait to jump until you're falling at a speed of at least 2(m/s). The problem is that 2(m/s) isn't very much, unless the fall is pretty short. Even from your 12.5m (about 40ft) you'd hit the ground at 16(m/s). A 2(m/s) jump cuts that to 14(m/s), better, but still pretty painful!

Read my post for the correct numbers. Rember the elevator is falling at 10m/s so the impact speed is 8m/s I still maintain that the jump will do more harm because of the poor postion of your body at impact.

The reason this problem got so complicated is that we all mixed physics with physiology.

I think the pure physics is this. Two masses are in free fall with one just above the other. The total momentum transferred to the Earth when both masses have landed, has to be the same, no matter what happens on the way down. If at anytime during the fall, the top mass can increase the downward speed of the bottom mass by applying a downward force to it, then the bottom mass will transfer more momentum to the Earth than it would have, so the top mass will transfer less and land more gently than it would have. It doesn't even matter when the force is applied (again, as long as applying it doesn't cause the top mass to start moving away from the ground).

Most of what you say here is nonsense. I do not think your jumping will have any significant effect on the motion of the elevator. Keep it simple, treat the problem as that of a falling body, because that is what it is.
I very carefully specified that the elevator is falling at a constant 10m/s NOT under free fall acceleration, simply because if you are in a free fall you will NOT be standing on the floor you will be floating somewhere inside the elevator, unless you have had some experience dealing with free fall it is not clear to me that you could orient yourself and push off in the right direction. This simply adds a lot of complexity, therefore I assumed that the elevator is at terminal velocity.

I think the physiology part is this: The best survival strategy is to give as much of your momentum as you can to the elevator and then bend your legs so that the impulse, integral(Fdt), that you apply to the Earth is spread over the maximum possible time, thus requiring the minimum possible force. But if the fall is from more than about 50 ft, even doing both of these won't prevent a pretty serious injury.

I do not disagree with this, what you say here is not the same as jumping, Though I have no clue what you mean by "give as much of your momentum to the elevator as you can" this is serious mumbo jumbo AFAIK.

 

[Michael D. Sewell]

I apologize if I have offended anyone by anything like a poor choice of words or by the tone of my writing. Besides, my attempts to produce witticisms and amuse people were perhaps misplaced.

outandbeyond2004,
Please don't apologize. I owe you an apology. My tone was too harsh and I was too sarcastic. I'm truly sorry.

The point I was trying to make is that many of us seemed to be more interested in argumentation than analysis. When discussing physics we all share an obligation to be realistic. We had people entertaining the idea of jumping upward at velocities that were not attainable. The discussion was getting foolish. This is physics forums, not a comic book.

We are not speculating on something that has never happened before. The statistics on accidents involving falls are available. The facts are known. Falls from 15 stories are not considered to be survivable-period.

Please accept my apology,
-Mike

 

[outandbeyond2004]

In response to Michael D. Sewell's apology and explanation of why he wrote as he did, I will accept his apology and let bygones be bygones. Now let me explain. I was not arguing for arguing's sake. Rather, I was simply exploring or trying out ideas or throwing them out. I don't deny I did not try hard to keep them realistic. However, when we are still trying to understand the problem thoroughly, it seems to me that we should allow our exploration to be somewhat unconstrainted. For one thing an idea may spark others. As our understanding matures, we can and should try to be more realistic, I agree. However, is it now time to be purely realistic? I am doubtful we really understand the problem now. It frequently happens that people overlook something that looks obvious only after the fact, you know, such as Integral's insight that the person's potentially-fatal kinetic energy must be dissipated slowly enough. Besides, we may find something interesting that has only a tenuous connection to the original question. Well, any thoughts about this post? Please don't be, shall we say, too nice.

 

[Michael D. Sewell]

Your point is well taken, and again I apologize. I am new to the internet and sometimes I find it hard to cope with not being able to read facial expressions and body language when communicating. When I re-read my post now, it looks a lot more malicious to me than when I wrote it. I am truly sorry, and I hope you will forgive me.

That being said, falls from 15 stories are not considered to be survivable. Many of you have presented, how should I say this... creative solutions to the problem. However, Integral is right, your solutions will not work. Falls from 15 stories are not considered to be survivable. -Mike

 

[outandbeyond2004]

Two ideas that does not seem to be good. Perhaps you can see a flaw in my reasoning or find improvements.

Integral appears to think my idea of taking off one's shoes and flinging them to the floor so as to propel oneself to the ceiling of the elevator is not workable, generally speaking. He's probably right. I want to consider a case that is clearly borderline. I would guess the elevator is moving 7 m/s and still accelerating, OK? I guess each floor is 5-7 meters. Clearly, the elevator can easily fall several floors by the time you take your shoes off, if you could ever acutally have any chance of doing so. Maybe 3 more floors by the time you throw the shoes, and yet 3 more floors by the time you arrive at the ceiling . . .

The other idea is this: You want to go to the 10th floor and you are at the 6th floor when you realize the elevator is going to fall. I think then that you brace your hands against the upper door frame until you know the elevator is falling freely. (I assume of course that you know the safety devices all are going to fail.) Then you push off it to flex your legs against the floor. Then you can jump to the ceiling. I am afraid this is iffy or worse, because you would need to go through the ceiling to the elevator top quickly for the manuever to do you any good. Besides, it won't work for people too short to touch the upper door frame.

 

[Michael D. Sewell]

Imho the first thing one would probably do in this situation is this .

The next thing one would do is this [zz)] , for a long, long time.

The EMTs would do this .

And the rest of us would feel this for you .

-Mike

wow, now my posts look like they belong in a comic book too...